Problem 101 - Precalculus Essentials

Question

The size of a television screen refers to the length of its diagonal. If the length of an HDTV screen is 28 inches and its width is 15.7 inches, what is the size of the screen to the nearest inch? (Section P.8, Example 8)

Step-by-Step Solution

Answer

The size of the screen to the nearest inch is 32 inches.

Step 1: Identifying The Given

In this problem, the length of the TV given is 28 inches and the width is 15.7 inches. This represents the two sides of a right triangle.

Step 2: Applying The Pythagorean Theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: \(c = \sqrt{a^2 + b^2}\), where 'c' represents the hypotenuse, 'a' and 'b' are the lengths of the two other sides. The hypotenuse or the diagonal of the TV will be calculated as follows: \(c = \sqrt{28^2 +15.7^2}\)

Step 3: Calculating the Size of the Screen

Once the numbers are added and their square root taken: \(c = \sqrt{784 + 246.49} = \sqrt{1030.49}\). The diagonal or the size of the screen will be approximately 32 (rounded to the nearest inch).